On the Complexity of Computing Generators of Closed Sets

  • Miki Hermann
  • Barış Sertkaya
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4933)


We investigate the computational complexity of some decision and counting problems related to generators of closed sets fundamental in Formal Concept Analysis. We recall results from the literature about the problem of checking the existence of a generator with a specified cardinality, and about the problem of determining the number of minimal generators. Moreover, we show that the problem of counting minimum cardinality generators is Open image in new window -complete. We also present an incremental-polynomial time algorithm from relational database theory that can be used for computing all minimal generators of an implication-closed set.


Relational Database Minimal Generator Truth Assignment Formal Context Formal Concept Analysis 
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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Miki Hermann
    • 1
  • Barış Sertkaya
    • 2
  1. 1.LIX (CNRS, UMR 7161), École Polytechnique, 91128 PalaiseauFrance
  2. 2.Institut für Theoretische Informatik, TU DresdenGermany

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